WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE

HANALIOGLU, Z.; KHANIYEV, T.; AGAKISHIYEV, I.

WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE

Z. HANALIOGLU, (Karabük Üniversitesi, Aktüerya ve Risk Yönetimi Bölümü, Karabük, Türkiye)

T. KHANIYEV, (TOBB ETÜ, Mühendislik Fakültesi, Endüstri Mühendisliği Bölümü, Ankara, Türkiye)

I. AGAKISHIYEV (Institute of Cybernetics of Azerbaijan National Academy of Sciences, B. Vahabzade Str. 9, AZ 1141, Baku, Azerbaijan.)

TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics

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Yıl: 2015 Cilt: 5 Sayı: 1 Sayfa Aralığı: 61 - 73 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE

Öz:

In this study, a semi-Markovian random walk process (X(t)) with a discrete interference of chance is investigated. Here, it is assumed that the ζn, n = 1, 2, 3, ..., which describe the discrete interference of chance are independent and identically distributed random variables having restricted normal distribution with parameters (a, σ2). Under this assumption, the ergodicity of the process X(t) is proved. Moreover, the exact forms of the ergodic distribution and characteristic function are obtained. Then, weak convergence theorem for the ergodic distribution of the process Wa(t) ≡ X(t)/a is proved under additional condition that σ/a → 0 when a → ∞.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	HANALIOGLU Z, KHANIYEV T, AGAKISHIYEV I (2015). WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE. , 61 - 73.
Chicago	HANALIOGLU Z.,KHANIYEV T.,AGAKISHIYEV I. WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE. (2015): 61 - 73.
MLA	HANALIOGLU Z.,KHANIYEV T.,AGAKISHIYEV I. WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE. , 2015, ss.61 - 73.
AMA	HANALIOGLU Z,KHANIYEV T,AGAKISHIYEV I WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE. . 2015; 61 - 73.
Vancouver	HANALIOGLU Z,KHANIYEV T,AGAKISHIYEV I WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE. . 2015; 61 - 73.
IEEE	HANALIOGLU Z,KHANIYEV T,AGAKISHIYEV I "WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE." , ss.61 - 73, 2015.
ISNAD	HANALIOGLU, Z. vd. "WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE". (2015), 61-73.

APA	HANALIOGLU Z, KHANIYEV T, AGAKISHIYEV I (2015). WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 5(1), 61 - 73.
Chicago	HANALIOGLU Z.,KHANIYEV T.,AGAKISHIYEV I. WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics 5, no.1 (2015): 61 - 73.
MLA	HANALIOGLU Z.,KHANIYEV T.,AGAKISHIYEV I. WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, vol.5, no.1, 2015, ss.61 - 73.
AMA	HANALIOGLU Z,KHANIYEV T,AGAKISHIYEV I WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics. 2015; 5(1): 61 - 73.
Vancouver	HANALIOGLU Z,KHANIYEV T,AGAKISHIYEV I WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics. 2015; 5(1): 61 - 73.
IEEE	HANALIOGLU Z,KHANIYEV T,AGAKISHIYEV I "WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE." TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 5, ss.61 - 73, 2015.
ISNAD	HANALIOGLU, Z. vd. "WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE". TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics 5/1 (2015), 61-73.